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Suppose that (Yi, Xi) satisfy the assumptions we made in the regression analysis. A random sample...

Suppose that (Yi, Xi) satisfy the assumptions we made in the regression analysis. A random sample of size n = 250 is drawn and yields

Yi =5.4 + 3.2×Xi, R2 =0.26, SER=6.2 (3.1) (1.5)

(i) TestH0 :β1 =0vs. H1 :β1 ̸=0atthe5%level.

(ii) Construct a 95% confidence interval for β1.

(iii) Suppose you learned that Yi and Xi were independent. Would you be surprised? Explain.

(iv) Suppose that Yi and Xi are independent, and many samples of size n = 250 are drawn, regressions estimated and the parts (a) and (b) answered. In what fraction of samples would the value β1 = 0 be included in the confidence interval from the second part.

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Expert Solution

Rahul Sunny answered 1 hour ago
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